\newproblem{lay:4_5_13}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.5.13}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Determine the dimensions of $\mathrm{Nul}\{A\}$ and $\mathrm{Col}\{A\}$ for the matrix 
	\begin{center}
		$A\begin{pmatrix}1 & -6 & 9 & 0 & -2 \\ 0 & 1 & 2 & -4 & 5 \\ 0 & 0 & 0 & 5 & 1 \\ 0 & 0 & 0 & 0 & 0\end{pmatrix}$
	\end{center}
}{
  % Solution
	The basis of the null space is formed by those non-pivot columns, in the case of $A$, the third and fifth columns. So, the dimension of $\mathrm{Nul}\{A\}$ is 2.
	The basis of the column space is formed by the pivot columns, in this case, the first, second and fourth columns. So, the dimension of $\mathrm{Col}\{A\}$ is 3.
}
\useproblem{lay:4_5_13}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
